feat(KB-168): remove legacy public/ directory and server fallback

- Delete public/index.html, public/style.css, and public/board.js legacy assets
- Remove public/ fallback from server.ts clientDir resolution chain
- Simplify clientDir to fall through to client/ instead of public/
- Add no-legacy-public test asserting public/ files and server references are gone

packages/dashboard/app/__tests__/no-legacy-public.test.ts

@@ -0,0 +1,31 @@
+import { describe, it, expect } from "vitest";
+import { existsSync, readFileSync } from "fs";
+import { resolve } from "path";
+
+describe("legacy public/ directory removal", () => {
+  const publicDir = resolve(__dirname, "../../public");
+
+  it("public/style.css does not exist", () => {
+    expect(existsSync(resolve(publicDir, "style.css"))).toBe(false);
+  });
+
+  it("public/board.js does not exist", () => {
+    expect(existsSync(resolve(publicDir, "board.js"))).toBe(false);
+  });
+
+  it("public/index.html does not exist", () => {
+    expect(existsSync(resolve(publicDir, "index.html"))).toBe(false);
+  });
+
+  it("server.ts clientDir resolution does not reference 'public'", () => {
+    const serverSrc = readFileSync(
+      resolve(__dirname, "../../src/server.ts"),
+      "utf-8",
+    );
+    // Extract the clientDir resolution block (from "const clientDir" to the semicolon)
+    const match = serverSrc.match(/const clientDir[\s\S]*?;/);
+    expect(match).toBeTruthy();
+    expect(match![0]).not.toContain('"public"');
+    expect(match![0]).not.toContain("'public'");
+  });
+});